Why are our stars bigger than the pros?

I've often wondered why the stars in my images, particularly of small things like galaxies, are big compared to an image taken by a pro with a super-expensive telescope. And if the stars are bigger, this means the fine details in the galaxy itself are worse. For galaxies, I often have to crop the image and resize to get a nice field of view showing only the galaxy. I assumed big-time astrophotograhers had to do the same thing, right? Wrong.

I thought the difference could be due to a number of things: better coatings on their mirrors, better seeing conditions, better tracking, better cameras. But I don't think it is. I think it actually comes down to Physics -- optics to be specific.

An image has two properties that are important here: (1) The best-case star size (detail), and (2) field of view. The smaller the stars, the more details the image will have. And, the tighter the field of view, the more "zoomed in" the image will be. Ideally, you want the smallest field of view and the smallest star size. What does that take?

To get the smallest stars possible, you calculate your "diffraction limit". This is the spot size of a star under perfect conditions (perfect seeing, perfect mirror, etc.). The formula looks like this:

Spot size = f-ratio * 2.44 * 0.53

This is for green light (0.53), which is in the middle of the spectrum. So, for my f/4.9 telescope, the diffraction spot size is:

Spot size = (4.9) * 2.44 * 0.53 = 6.47um

No matter how good the seeing is, I cannot get stars smaller than this, and thus I will not be able to see any details in the galaxies smaller than this. This isn't too bad since the pixels on my ST-8300 are 5.4um. I don't want the stars to be much bigger than my pixels because then I'm just "over sampling", but that's another discussion.

Now that I know my best-case scenario star/detail size, I want a tight field of view so I'm really zoomed into my galaxy. As it turns out, the field of view is dependent only on the focal length of the telescope. The equation looks something like this:

FOV = ((pixel size/focal length) * 206.3) * # pixels

So, for my 1000mm FL telescope and the 5.4um pixels (3362 of them horizontally), I get a FOV of:

FOV = ((5.4/1000) * 206.3) * 3362 = 62 arcminutes

Hmm, that's a little too wide for a small galaxy. For example, the relatively large Whirlpool Galaxy (M51) is only 18 arcminutes. Okay, so I throw on the TeleVue 2x PowerMate to double my focal length, right? That gives me a FOV of:

FOV = ((5.4/1989) * 206.3) = 31 arcminutes

because the PowerMate ups the focal length to 1,989mm. That's better, but what happened to the star size? It's now:

Spot size = (10) * 2.44 * 0.53 = 13 arcseconds,

compared to 6.47 arcsec before. Phooey. I get a good FOV, but my stars are almost twice as big. That's no better than just cropping the image and resizing!

The answer is to go to a LONG FOCAL LENGTH with a SMALL f-ratio. Since the f-ratio is:

f-ratio = focal length/aperture,

The only way to do that is by increasing the aperture while increasing the focal length.

Thus, big telescopes are not just for collecting a lot of photons, but they also give more detail. This may have been obvious to others, but I once thought that my small 8" scope, given enough integration time, could collect as many photons as a bigger scope and thus produce the same level of final image.

Your M51 is a great image. Can someone do better with a mountain top observatory and a $100,000 telescope? Apparently, yes. My advice is, "Don't sweat that." In this case what separates you from the pro is a hell of a lot of money. That's it.

I'm a bit curious though at to the apples to oranges comparison and star size subject line.

I think it important to say that a 'pro' with your scope or another of similar make and etc might end up with the same results if not adding in possibility of post processing the star shapes and star masking and other modification technique. Your image is really nice!

Beyond that, quality of optics / type of optic system (geometric optic differences) are critical to the governing 'possible' PSF and MTF of the what the system is capable of if perfectly cooled and collimated, and I'd include any correctors in the trane there. It is in the fine detail that quality otics can 'strut their stuff' when conditions permit. Purely my opinion but I feel they (really good optics) perfrom better in average to poor conditions as well.

I think imaging can 'smooth out the seeing conditions' to a point but not beyond, for brighter point sources it is less of an issue (? and in ways maybe not as they are high amplitude?) but as the source brightness decrease the effect of turbulance and scatter become more significant - depending on the ratio of pixel size and sensitivity other consideration in resulting processed final contrast ratio. As you increase the size of the optic you are also increasing possible sensitivity to atm conditions? I mention this only because most of really good images I see done with larger optics are done at a relatively small geography - like Mr. Croman in New Mexico.

I'm in agreement with your conclusion to a point if what you are referring to is the Rayleigh/Dawes/Sparrow resolution (and MTF and PSF and idea of working function of the optic) and possible sensitivity as you proceed to limiting magnitude with respect to aperture but not with focal ratio - focal ratio has more to do with the point source spot size / pixel size ratio of the detector, or at what ratio/size (can look at as a mesh function at slice of light cone) the resolution of the optic is presented to the sensor...

At least if I understand what you are presenting here. I agree it's important to understand what each component of the system can do (and I include seeing / sky conditions as an equal player as a component when considering the weaker sources) and where that components responsibility for the final product start and stop. We have a lot of say in how we choose components for the imaging system, unfortunately we can't steady out the seeing conditions to eek out the best possble performance from them. There's an interesting wikipedia page about this here, and a more technical look here.

It's an interesting topic, and in ways a complicated one - I think it's great you are trying to distill it down into what is possible 'real world' in the final product and not only in the theoretical paper whipping of it all. For some time I've been debating to get the AT 10" f/4 imaging newt on several levels (the cost is the least impacting as it's very affordable) - it's being so close to the jet stream that makes hesitate.

I thought the difference could be due to a number of things: better coatings on their mirrors, better seeing conditions, better tracking, better cameras. But I don't think it is. I think it actually comes down to Physics -- optics to be specific.

You are making a mistake by assuming it's only one factor. Add in processing technique, exposure time, image calibration; each one is a significant factor. The pro's are just able to do all of these things well.

It's kind of like saying that if you find 5 very tall guys you have a pro basketball team.

Many of these guys you describe as "Pros" are really just very good amateurs. Very few of them make their living off astroimaging. Yes, a few pick up travel expenses now and then with their workshops and some sell their prints online or make tutorial programs and put them on DVD. But few make a living off the images. In real life they are pediatricians, computer geeks, retired (mostly) guys and (some) ladies, unemployed people, etc. They are just like everybody else except for an extraordinary dedication, talent, and application of skills. (Which, admittedly makes them different from me and a few others in the mainstream population.) And when they get really good, they start buying better equipment. But the incremental improvement in the images decreases rapidly after a certain point compared to the additional cost of the equipment.

Second, good big equipment helps, but, really, an awful lot of processing techniques go into it. I know plenty of people with all the perfect equipment and good observing sites that turn out stuff not much better than mine.

Third, as I have been told so many times by some very good imagers......"Its not a competition."

We are going to have a special Imaging star party in February out at our observing site, and are inviting all the imagers to sit down and process a single set of data, and see how the pictures vary. I will bet you a dollar that (on first attempt) my star images will be twice as fat as the good guys--using the same data. Of course by the end of the session, I will have learned what they do to keep them from bloating. (That is February 1,2, at GMARS, Landers California.....rivastro.org for info on GMARS)

Barry, you are correct in your assessment that larger aperture provides increased resolution. However, this doesn't by itself explain why folks with bigger scopes get better results.

The first thing to consider is seeing conditions. For almost all of us, seeing conditions start to limit resolution long before we get to our diffraction limits--even of we have relatively small scopes. I have imaged using scopes from 3" in aperture to 12.5" in aperture, and the best resolution I ever got was with a 6" scope! The night in question happened to have superb seeing conditions. If I ever get a night like that with my 12.5" scope, I'll be a happy camper.

The real trick isn't having a giant scope. It's having a system that is of high enough quality and having good enough technique to take advantage of what the seeing will allow. If you live under 3" skies, an 8" scope can probably give you all the resolution of a 20", but only if it is well collimated, in perfect focus, we'll guided, etc. want to take advantage of that 20"? Better go somewhere with good seeing.